Nonlinear buckling may be evaluated in SAP2000 using Nonlinear static analysis. This procedure takes an iterative approach while implementing P-Delta and Large-Displacement effect. Structural response is shown by plotting selected joint displacements against load application. A softening behavior may be observed in this plot, indicating the onset of buckling, and the condition of instability which follows.
Modeling tips
- When analyzing symmetrical structures, users may need to introduce either a geometric or loading imperfection to initiate buckling.
- In the load-case definition, users should request multiple output steps to improve convergence, and to better indicate buckling response.
- If a structure loses load-carrying capacity, users should implement displacement control, rather than load control. This refers to the load-case control definition, and not how the load is actually applied.
- Users may need to tighten convergence tolerance, possibly to the order of 1e-6.
- Elements should be small enough to capture geometric nonlinearity. Four to eight frame or shell elements are typically necessary per span.
- When instability is severe, users should convert nonlinear static analysis to direct-integration time-history analysis.
Difference between Linear and Nonlinear static buckling analyses
During Linear buckling analysis, perturbations are applied to the undeformed configuration of a structure. A specified set of loads are observed for which deflections could induce instability under P-Delta effect. Linear buckling analysis produces a set of buckling factors and corresponding mode shapes. When loading is multiplied by these buckling factors, the resultant scaled loading conditions represent those which induce buckling. Similarly, the mode shapes are normalized displacement sets which indicate the configuration of the buckled structure.
During Nonlinear static buckling analysis, the total load is applied incrementally. Stiffness and response are evaluated at each increment. Between each displacement step, stiffness may change due to the following effects:
- P-Delta effect, which involves large tensile or compressive stresses on transverse bending and shear behavior;
- Large-Displacement effect, where deformed configuration is considered when assembling the equilibrium equations; and
- Nonlinear material behavior, where performance incorporates inelastic element response. SAP2000 implements material nonlinearity using frame hinges and nonlinear layered-shell elements.
Because Nonlinear static buckling analysis considers material nonlinearity in generating buckling response, results are often more realistic than those of Linear buckling analysis. The results of Nonlinear static analysis are indicated by a plot of deformed configuration against load application. This plot displays the softening behavior which indicates buckling onset.
The CSI Analysis Reference Manual is an excellent resource for information on buckling. Users are recommended to review the following chapters:
- Analysis Cases > Linear Buckling Analysis, page 315
- Geometric Nonlinearity > Overview, page 365
- Geometric Nonlinearity > P-Delta Effect, page 369
